# How to Compare Paired Data with R

When testing differences between two data groups in R, you can have either paired or unpaired data. Paired data comes from experiments where two different treatments were given to the same subjects.

For example, researchers gave ten people two variants of a sleep medicine. Each time the researchers recorded the difference in hours of sleep with and without the drugs. Because each person received both variants, the data is paired. You find the data of this experiment in the dataset sleep, which has three variables:

A numeric variable extra, which give the extra hours of sleep after the medication is taken

A factor variable group that tells which variant the person took

A factor variable id that indicates the ten different test persons

Now they want to know whether both variants have a different effect on the length of the sleep. Both the t.test() and the wilcox.test() functions have an argument paired that you can set to TRUE in order to carry out a test on paired data. You can test differences between both variances using the following code:

> t.test(extra ~ group, data=sleep, paired=TRUE)

This gives you the following output:

Paired t-test data: extra by group t = -4.0621, df = 9, p-value = 0.002833 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -2.4598858 -0.7001142 sample estimates: mean of the differences -1.58

Unlike the unpaired test, you don’t get the means of both groups; instead, you get a single mean of the differences.